249 lines
9.4 KiB
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249 lines
9.4 KiB
HTML
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HREF="index.shtml">A dynamical model for</A>
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<B> Previous:</B> <A NAME="tex2html68"
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HREF="node4.html">The dynamical model</A>
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<H1><A NAME="SECTION00050000000000000000"></A>
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<A NAME="s:results"></A>
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<BR>
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Results
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</H1>
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The synthetic ECG (Fig. <A HREF="node5.html#f:ecgsynthetic">5</A>) illustrates
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the modulation of the QRS-complex due to RSA.
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Observational uncertainty is incorporated by adding normally
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distributed measurement errors with mean zero
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and standard deviation 0.025 mV (Fig. <A HREF="node5.html#f:ecgcomparison">6</A>a),
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yielding a similar signal to a segment of real ECG from a normal human
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(Fig. <A HREF="node5.html#f:ecgcomparison">6</A>b).
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In order to illustrate the
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dynamics of the RR-intervals obtained from this synthetic ECG, peak detection
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was used to identify the times of the R-peaks.
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In the noise-free case, a simple algorithm which looks for local maxima
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within a small window is sufficient. For ECGs with noise and artefacts it
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may be necessary to use more complicated methods [<A
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HREF="node8.html#pan85">2</A>,<A
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HREF="node8.html#kaplan91">3</A>].
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A comparison between the continuous process with power spectrum <IMG
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WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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SRC="img2.png"
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ALT="$S(f)$">
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given by (<A HREF="node4.html#e:Sf">3</A>) and the piecewise constant
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reconstruction of the RR-process obtained from the R-peak detection
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(Fig. <A HREF="node5.html#f:rrinout">7</A>) illustrates the measurement errors that
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arise when computing heart rate variability statistics from
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RR-intervals.
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The RR-intervals (Fig. <A HREF="node5.html#f:rrsynthetic">8</A>a) and corresponding
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instantaneous heart rate (Fig. <A HREF="node5.html#f:rrsynthetic">8</A>b)
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in units of beats per minute (bpm)
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for a mean of 60 bpm and standard deviation of 5 bpm
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display variability due to both RSA and Mayer waves.
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A spectral estimation technique
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for unevenly sampled time series, the Lomb periodogram
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[<A
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HREF="node8.html#press92">15</A>,<A
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HREF="node8.html#laguna98">16</A>], was used to calculate the power
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spectrum (Fig. <A HREF="node5.html#f:rrsynthetic">8</A>c) from the RR tachogram,
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derived from 5 minutes of data as recommended
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by [<A
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HREF="node8.html#malik95">7</A>,<A
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HREF="node8.html#eursoccard96">10</A>].
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Despite the loss of information in going from the continuous process to the
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piecewise constant reconstruction, a comparison between Fig. <A HREF="node4.html#f:Sf">4</A> and
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Fig. <A HREF="node5.html#f:rrsynthetic">8</A>c illustrates that it is still
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possible to obtain a reasonable estimate of the power spectrum.
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<DIV ALIGN="CENTER"><A NAME="f:ecgsynthetic"></A><A NAME="168"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
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ECG generated by dynamical model: (a) 10 seconds and (b) 50 seconds.</CAPTION>
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<TR><TD><IMG
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WIDTH="352" HEIGHT="275" BORDER="0"
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SRC="img63.png"
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ALT="\begin{figure}
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\centerline{\psfig{file=ecgsynthetic.eps,width=7.75cm}}
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\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<DIV ALIGN="CENTER"><A NAME="f:ecgcomparison"></A><A NAME="173"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 6:</STRONG>
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Comparison between (a) synthetic ECG with additive normally
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distributed measurement errors and (b) real ECG signal from a normal human.</CAPTION>
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<TR><TD><IMG
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WIDTH="352" HEIGHT="275" BORDER="0"
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SRC="img64.png"
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ALT="\begin{figure}
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\centerline{\psfig{file=ecgcomparison.eps,width=7.75cm}}
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\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<DIV ALIGN="CENTER"><A NAME="f:rrinout"></A><A NAME="296"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7:</STRONG>
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Reconstruction of RR-process from R-peak detection:
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the underlying RR-process generated using (<A HREF="node4.html#e:Sf">3</A>) (black line)
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and the RR-interval time series obtained using R-peak
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detection of the synthetic ECG (grey line).</CAPTION>
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<TR><TD><IMG
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WIDTH="352" HEIGHT="275" BORDER="0"
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SRC="img65.png"
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ALT="\begin{figure}
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\centerline{\psfig{file=rrinout.eps,width=7.75cm}}
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\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<DIV ALIGN="CENTER"><A NAME="f:rrsynthetic"></A><A NAME="298"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 8:</STRONG>
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Analysis of RR-intervals from R-peak detection of the ECG signal
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generated by the dynamical model (<A HREF="node4.html#e:pqrst">1</A>) with mean heart rate 60 bpm
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and standard deviation 5 bpm: (a) RR-intervals,
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(b) instantaneous heart rate and (c) power spectrum of the RR-intervals.
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Note the two active frequencies belonging to RSA (0.25 Hz) and Mayer
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waves (0.1 Hz).</CAPTION>
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<TR><TD><IMG
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WIDTH="352" HEIGHT="272" BORDER="0"
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SRC="img66.png"
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ALT="\begin{figure}
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\centerline{\psfig{file=rrsynthetic.eps,width=7.75cm}}
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\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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An increase in the RR-interval implies that the trajectory has more time to
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get pushed into the peak and trough given by the R and S events.
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This is reflected by the strong correlation between the RR-intervals and the
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RS-amplitude as shown in Fig. <A HREF="node5.html#f:rsrr">9</A>. A technique for deriving a measure
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of the rate of respiration
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from the ECG has been proposed [<A
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HREF="node8.html#moody85">5</A>,<A
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HREF="node8.html#moody86">6</A>].
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This ECG-derived respiratory signal (EDR) is of clinical use in
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situations where the ECG, but not respiration, is recorded.
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The synthetic ECG provides a means of testing the robustness of such
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techniques against noise and the effects of different sampling frequencies.
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<DIV ALIGN="CENTER"><A NAME="f:rsrr"></A><A NAME="190"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 9:</STRONG>
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RS-amplitudes versus RR-intervals for the synthetic ECG.</CAPTION>
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<TR><TD><IMG
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WIDTH="351" HEIGHT="275" BORDER="0"
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SRC="img67.png"
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ALT="\begin{figure}
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\centerline{\psfig{file=rsrr.eps,width=7.75cm}}
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\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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As a consequence of constructing the model with a variable angular frequency
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<IMG
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WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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SRC="img61.png"
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ALT="$\omega(t)$">, the time taken to
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move from the Q event to the T event, known as the QT-interval, varies with
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the RR-interval on a beat-to-beat basis.
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The relationship between the QT-interval and the
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RR-interval is linear as shown in Fig. <A HREF="node5.html#f:qtrr">10</A>.
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Such a linear relationship has been reported for real ECGs and
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has been used to calculate a corrected QT-interval [<A
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HREF="node8.html#davey99">4</A>].
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It is interesting that this relationship is a direct consequence of the
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model. Furthermore it may be possible to use the model to assess how much of
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the variation in the QT-interval is due to RR-interval variability so that
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this effect can be factored out.
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<DIV ALIGN="CENTER"><A NAME="f:qtrr"></A><A NAME="197"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 10:</STRONG>
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QT-intervals versus RR-intervals for the synthetic ECG.</CAPTION>
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<TR><TD><IMG
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WIDTH="352" HEIGHT="275" BORDER="0"
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SRC="img68.png"
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ALT="\begin{figure}
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\centerline{\psfig{file=qtrr.eps,width=7.75cm}}
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\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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HREF="node6.html">Conclusions</A>
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<B> Up:</B> <A NAME="tex2html74"
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HREF="index.shtml">A dynamical model for</A>
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<B> Previous:</B> <A NAME="tex2html68"
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HREF="node4.html">The dynamical model</A>
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<ADDRESS>
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2003-10-08
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